A frustum is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.

The surface area is the total area of all the surfaces of a closed 3D shape. The surfaces include all faces and any curved surfaces.

Surface area of a frustum of a cone

Maths

In this unit, pupils have increased their knowledge of volume which is used in the compound measures unit as the formula for density involves volume. 

In the prior unit, pupils built upon their learning of the area of different shapes. In this unit, pupils will continue to further develop their understanding of shapes by considering surface area and volume of pyramids, spheres and cones.

2D and 3D shape: surface area and volume (pyramids, spheres and cones)

The area of the curved surface of this frustum is {{ }}𝜋 cm². Leave your answer in terms of 𝜋.

The total surface area of this frustum is {{ }}𝜋 cm². Leave your answer in terms of 𝜋.

Work out the length of the side marked $$x$$ on this frustum.

Find the area of the curved surface of this frustum. Leave your answer in terms of 𝜋.

A __________ is the 3D shape made from a cone by making a cut parallel to its circular base and removing the resultant smaller cone.

The left-hand cone is split into a smaller cone and a frustum. Match each length labelled a - c to its value.

The diagram shows a side elevation of a frustum. Find the volume of the large cone that the frustum is cut from. Give your answer correct to 3 significant figures.

The diagram shows a side elevation of a frustum. Find the volume of the frustum. Give your answer correct to 3 significant figures.

A cone is cut into a frustum of height 20 cm and a small cone. The radius of the base of the frustum is 15 cm and the radius of its top is 12 cm. The height of the small cone is {{ }} cm.

The diagram shows a large cone with a frustum of height 20 cm and a small cone. The radius of the frustum base is 15 cm and the radius of its top is 12 cm. The volume of the frustum is {{ }}𝜋 cm³.

This lesson will be removed by end of Summer Term 2025.

Surface area of a frustum of a cone

Lesson outcome

This lesson will be removed by end of Summer Term 2025.